Analyzing social change requires detecting patterns of continuity and difference over time. While time-series clustering offers a valuable approach, existing techniques are often limited by assuming fixed cluster definitions and static assignments of entities to clusters. To address these limitations, we introduce a unified framework of temporal clustering methods that allows for both dynamic cluster definitions and the transition of entities between clusters, generalizing and extending previous work. We also provide new algorithms for this dynamic clustering that optimize global objectives, with optional constraints on the transitions of entities across clusters. This framework expands the methodological toolkit for analyzing social change, and we provide guidelines for its application. We illustrate our approach with three case studies: polarization of social and political attitudes across U.S. states; cross-national cultural change; and the evolution of neighborhood business patterns. We conclude with directions for further research.
Liang et al. (2026) studied this question.